Up the Ladder

This ladder game provides a fun challenge that builds understanding of the place value of 3-digit numbers as well as practice in ordering those numbers.
The key learning opportunity comes from discussion of the strategies used to place numbers so that a player gives themselves the best chance of winning. This involves putting numbers close together on the ladder if they are close in size. It also involves placing smaller numbers nearer the bottom of the ladder and larger numbers nearer the top.
The importance of the digit in the hundreds place should be discussed after the students have played the game a few times.
The students should be encouraged to track the numbers that have been used so that they think about the possibilities left to them. For example, if all three nines have been used, they will not be able to make a number in the nine hundreds until all the cards have been used and the pack is reshuffled.
This type of game is ideal to use as an independent activity in a learning centre after it has been used for instructional purposes.

Activity

Have the students discuss the aspects that will influence Vanna’s and Logan’s chances. These aspects are the digits already chosen for this round and the number of winning digits still available for selection.
If the students analyse the numbers already on the ladder, they should realise that Vanna and Logan have gone through the whole pile of cards once, and on the second time through, they have six cards left for the tenth round. (In practice, the students will probably find that, in their own games, they will need to go through the cards more than twice to fill their 10 rungs, especially at the start and until they get used to using strategies for ordering their numbers.) After Vanna and Logan have drawn two cards each, the two cards left are a 0 and a 5. Vanna has a 50 percent chance of winning on this round because she can win if she draws the 5 (to make 593 or 539). Logan cannot win with either card because he needs a 2 or a 3 (to make a number
between 407 and 218).

Variations and Extensions

This game can be extended to 4-digit numbers or decimal numbers if a decimal point is placed on each rung. The range could be reduced by changing the top and bottom numbers on the ladder. The students could explore the effect on the game if the number of sets of digit cards used is changed.

Answers to Activity

A game ordering numbers between 100 and 1 000
Activity
Vanna. She has a 50% chance of winning. (There are two cards left, a 0 and a 5, and she needs to draw the 5.) Logan has no chance of winning in this round because he cannot use the 1 or the 5.